But ... they already do so.
Here for example there are is a text adopted on the latest meeting from the European Parliament.
https://www.europarl.europa.eu/doceo/document/TA-9-2020-0222_EN.html
It's translated in all official 24 EU languages (on top right you can switch). Even in Irish, which only has 40,000 native speakers. Each country may choose one official language, and Ireland chose Irish (which is pretty much a dead language over there), because the UK already chose English.
All law and official documents are translated in these languages.
And also all plenary meetings and other important speeches are live translated into all of these languages.
It's actually a significant cost and bureaucratic nightmare, because accurately translating law texts is really hard to avoid discrepancies.